I was thinking to start from a logical perspective, maybe a combination of two words three that ideally could stand for x3 (7x3) and the word week itself, maybe in another language?
French: "Trois semaines"
Spanish: "Tres semanas"
Italian: "Tre settimane"
German: "Drei Wochen"
Portuguese: "Três semanas"
Russian: "Три недели" (Tri nedeli)
Japanese: "三週間" (Sanshūkan)
Korean: "세 주" (Se ju)
Chinese (Mandarin): "三周" (Sān zhōu)
Esperanto: "tri semajnoj" that is already a good mix itself
Latin: "tres septimanae"
So there'are pattern here, one with tr + se and the second with Sx + xu where the x is a written reinterpretation of the same sound. Maybe... that's just me fantasizing. Not really an expert in phonetic languages but it fun to play around.
Anyway, if I stay o the wester pattern TreSem come up to me tresem then? Mmm.. there's already TRESemme that is a english respelling of "beloved" (French: très-aimé) that includes the surname of its namesake.
x+xu where thexis a written reinterpretation of the same sound. Maybe... that's just me fantasizing. Not really an expert in phonetic languages but it fun to play around.